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The Theory and Applications of Iteration Methods: 1st Edition (Hardback) book cover

The Theory and Applications of Iteration Methods

1st Edition

By Ioannis K. Argyros, Ferenc Szidarovszky

CRC Press

368 pages

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Hardback: 9780849380143
pub: 1993-09-15
$275.00
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eBook (VitalSource) : 9780203719169
pub: 2018-05-04
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Description

The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics.

Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.

Table of Contents

The Convergence of Algorithmic Models. The Convergence of Iteration Sequences. Monotone Convergence. Comparison Theorems. The Convergence of Newton Methods and Their Variants. The Monotone Convergence of Newton Methods and Their Variants. References. Index.

About the Series

Systems Engineering

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Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics
TEC009060
TECHNOLOGY & ENGINEERING / Industrial Engineering